APM346-2012 > Home Assignment 3

problem 3

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Thomas Nutz:
Could anyone give me a hint on how to integrate problem 3a)? In order to get rid of the absolute value I have to split up the integral and then the -inf to inf formulas don't work any more...

Thanks a lot!

Calvin Arnott:
Try completing the square and using the error function. It's a really messy integral.

Victor Ivrii:

--- Quote from: Calvin Arnott on October 08, 2012, 12:18:45 AM ---Try completing the square and using the error function. It's a really messy integral.

--- End quote ---
$\newcommand{\erf}{\operatorname{erf}}$
Yes, you need to consider  $\erf(z)$ as an elementary function (and there is no compelling arguments why trigonometric functions are considered as such but not many others. In fact there are plenty of important special functions coming often from PDE, more precisely, from separation of variables--not $\erf$ but many others).

Peishan Wang:
Should part (c) and part (d) be: solve the IBVP for x>0 or for all x? Thanks!

Victor Ivrii:

--- Quote from: Peishan Wang on October 08, 2012, 07:43:01 AM ---Should part (c) and part (d) be: solve the IBVP for x>0 or for all x? Thanks!

--- End quote ---

For $x>0$ only, I adjusted problem to make it explicit

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